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C13×C3⋊((C19⋊C3)⋊D7) #44527994

order31122
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊((C19⋊C3)⋊D7)
unambiguous semidirect productC3⋊(C13×(C19⋊C3)⋊D7)
unambiguous semidirect product(C19⋊C3)⋊(C13×D21)

Splittings

Fitting, socleC3×C7×C13×C19 ⋊ C2×C3
derivedC3×C7×C19 ⋊ C2×C3×C13
HallC3×C7×C13×C19⋊C3 ⋊ C2
HallC3×C13×C19⋊C3 ⋊ D7
HallC7×C13×C19 ⋊ C3×D3
HallC3×C7×C19⋊C3 ⋊ C2×C13
HallC13×C19 ⋊ C3×D21
HallC3×C19⋊C3 ⋊ C13×D7
HallC7×C19 ⋊ C3×D3×C13
HallC7×C13 ⋊ C3⋊(D19⋊C3)
SylowC19 ⋊ C3×C13×D21
SylowC7 ⋊ C13×C3⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC13C3⋊((C19⋊C3)⋊D7)
commutator, cosocle, hypocenterC3×C7×C19C2×C3×C13
FrattiniC1G
Fitting, socleC3×C7×C13×C19C2×C3
LCSG ▷ C3×C7×C19
UCSC1 ◁ C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5187

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 477);